laser based plasma diagnostic techniques: velocity...
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Laser based plasma diagnostic techniques:Velocity distribution by Laser Induced
Fluorescence (LIF) technique
Nader SADEGHI
LaboratoireInterdisciplinairede Physique (LIPhy, ex LSP) et LaboratoireInterdisciplinairede Physique (LIPhy, ex LSP) et Laboratoire des Technologies de la Microélectronique(LTM),
Université Joseph Fourier & CNRS Grenoble, B.P. 87, 38 402 St Martin d ’Hères (France)E-mail: Nader.Sadeghi@ujf-grenoble.fr
Principle of Laser Spectroscopy
Laser frequency is tuned to a specific transition of interest
1
2
Intensity
I 0(ν)
∼
LaserAbs.
νν0
I (ν)
Either in Laser Absorption or in Laser Induced Fluorescence techniques, spectral information comes from the first step:
absorption of photons
LIF
LaserAbs.
Principle of Laser Spectroscopy
Intensity
νν0
I 0(ν)
I (ν)
ν0
−= )()(
4)( 2
2
11
12 ννλγ
να ng
gn
hBAbsorption Coefficient
)(.))(
)(( 0 να
νν
lI
ILn =-From absorption signal
-From LIF signal )().()( ναν LaserLIF PI Φ≈
transition probability
α(ν) = Ν k Φ(ν)
Densitytraces Detection
Line profile Analysis
What can we learn by measuring α(ν) ?
probabilitytraces Detection Analysis
Φ(ν)
ν
Units used in spectroscopy
1 eV = 1.6 x 10-19 J = 8065 cm-1
300 kT = 207 cm-1
1 cm-1 = 30 GHz
c * λ∆c
Wavenumber
λν c=
2
*
λλν ∆=∆ c
Linewidth:At 563 nm, ∆λ =1 nm → ∆ν = 1000 GHz
Photon energy:λ = 500 nm 1/λ = 20000 cm-1
Different type of LasersFrequency fixed: (often used as pump laser)
- Ar +, Kr +, Nd-Yag, Excimer (XeCl), Cu, HeNe ….. ∆νL≅ 10 GHz
Tunable lasers:- Pumped by a laser: Dye, Ti:Sa, OPO (tuning range 10 to 100 nm)
Lasers available from 400 nm to µm (+ frequency doubling)
* Pulsed lasers: P up to 10 mJ, ∆ t ≈ 3 to 30 ns, ∆νL≥ 1 GHz* Pulsed lasers: P up to 10 mJ, ∆ t ≈ 3 to 30 ns, ∆νL≥ 1 GHzConvenient for frequency doubling and n photon transitions
* CW lasers: P= up to a few W, ∆νL ≈ 0.001 GHzConvenient for high resolution spectroscopy
- Diode laser: lasers available from 400 nm to 10 µm with
* tuning range up to 10 nm
* P= up to a few 10 mW, ∆νL ≈ 0.001 GHz(if single mode) They are more compact, easier to run and cheaper
How the line profile is related to the velocity distribution function?
Doppler shift: )/.1(0 cVkL
rr+=νν
c
Vkr
//
00
0 =∆=−ν
νν
νν
The frequency shift is related to only velocity along the laser propagation direction
zV V yx dVdVVfVfy z∫ ∫= .).()(
r
The measured velocity distribution function is an integral over the other two directions
)(.)( 0xVf
cf
νν =
Laser Absorption Spectroscopy
- provides sight of line averaged quantities
Laser Induced fluorescence
-has very high space resolution
LAS vsLIF
quantities
-has limited sensitivity
- Provides absolute density of absorbing species
- is very high sensitivity (a single atom can be excited many many times); photon counting
- But cannot provide absolute densities without a calibration method
Origin of optical saturation
• 1- Laser beam transfers a significant number of atoms from the lower to the upper state and
−= )()(
4)( 2
2
11
12 ννλγ
να ng
gn
hB α becomes no more proportional to n1
atoms from the lower to the upper state and n2 becomes no more negligible compared to n1.(short pulse lasers)
• 2- Atoms in the upper state are lost by radiation, or collisional transfers, to a 3rd state and atoms in the lower state are not renewed fast enough: the lower state becomes depleted.(cw lasers)
Rate equations governing the population densities N1 and N2 of states |1⟩ and |2⟩ are:
1
2
11,1112221211 )/1()(/ CNMkBNABdtdNq
qq +++−+= ∑τρρ
22,22321211122/ CNMkAABNBdtdNq
qq +
+++−= ∑ρρ
is is the Einstein coefficient for stimulated emission
we assume g1 = g2 , ρ is the energy density of the beam,
Ci accounts for the repopulation of state |i⟩ from different paths, including diffusion transport into the laser volume and radiative cascades
and
are the total relaxation rates of the states
21
30
122
121 8
Ah
Bg
gB
πλ==
∑∑ +=ℜ= q
qqloweri
i NkA ,222∑+=ℜq
qqNk ,111 1τ
in steady state, (dNi/dt=0) the density difference of states |1⟩ and |2⟩ is:
Where is in the absence of laser beam (ρ=0),
and*
12 /ℜ= ρBS is The saturation parameter
related to the mean relaxation rate:
)/( 2121* ℜ+ℜℜℜ=ℜ
)/( 1212
2
1
102
01
0 ℜ−ℜ−ℜ=−=∆ AgCC
gNNN
)1(21
1212021 ℜ+ℜ
ℜ+−ℜ+∆=−=∆ gASNgNNN
:2121
Larger S is, lower the measured population will be
The resulting population density in the lower state is:
When ρ → 0, For ρ → ∞1
11 ℜ
= CN
2212
211
)(ℜ+−ℜ
+=gA
CCgN
)(][)/()/(
211212
*212
*21
1 RRgRARSAgSCRgSC
N +++−ℜ++ℜ+= When
C2 0 )(][)/(
211212
*21
1 RRgRARSRgSC
N +++−ℜ+=
Intensity of Laser Induced Fluorescence signal
1
2
LIF signal is proportional to N2 density given by:
221
1223123223 ),,(
ℜ+∝∝
ρρ
B
BARVElNANI
When LIF is used to determine the relative populations of two different species, m and n:populations of two different species, m and n:
At low laser power limit, the LIF signal ratio is:
2,
2,
23
23
12
12
1
1
23
23
)(
)(
)32;(
)32;(
n
m
n
m
n
m
n
m
A
A
B
B
nN
mN
nI
mI
ττ
=→→
At high laser power limit, the LIF signal ratio is:
n
m
n
n
m
m
n
m
A
A
g
g
g
g
nN
mN
nI
mI
23
23
,2
,1
,1
,2
1
1
23
23
)(
)(
)32;(
)32;(
=
→→
τ could be p and T dependent
Calculation of the saturation parameter S1- Pulsed laser:
λ= 589 nm ; τ2=16 ns ; A21=6 106 s-1 ; R2=1/τ2=6.25 107 s-1;
R1=(1/transit time inside a beam of φ=2 mm)=(0.5 km.s-1)/(2 mm)=2.5 105 s-1 g2= g1
Laser pulse: P=1 mJ; ∆L= 4 ns pulse duration; ∆νL= 0.2 cm-1= 6 GHz; φ=2 mm
∆L< τ2
J.s/m3
m3/J/s2 s-119639
213
10*3.710*6*)10*589( ===
−λ AB
898239
3
10*410*6*10*3*)10(**10*4
10
***−
−−
−
==∆∆
=πν
ρLL cs
P
521 10*5.2=== RRR
Rm3/J/s2 s-1
B12*ρ= 3* 1012 s-1 >> R2 Very Big
Then immediately during the laser pulse N2 = N1 = 0.5* N10
GHz Broader than the laser line
If : τ2=5 ns; A21=2 107 s-1 ; R2=1/τ2=2 108 s-1; P=1 mJ; ∆L= 40 ns > τ2
B12*ρ= 1* 1012 s-1 >> R2 Very Big
Then in the end of the laser pulse
1934
2112 10*3.7
10*6.6**8
10*6*)10*589(
8=== −ππ
λh
AB
51
21
21 10*5.2==+
= RRR
RRR
35*35001* ==+= δνδνδν SS
6
1
12 10*4* ==
R
BS
ρ
01
012
0112 *018.0)4()2/( NExpNRExpNNN L =−=∆−==
7
1
12 10*2.1* ==
R
BS
ρ
Calculation of the saturation parameter Scw laser:
λ= 589 nm; τ2=16 ns ; A21=6 106 s-1 ; R2=1/τ2=6.25 107 s-1;R1=(1/transit time inside a beam of φ=2 mm)=(0.5 km.s-1)/(2 mm)=2.5 105 s-1 g2= g1
Laser power: P=10 mW; ∆νL= 1 MHz <<1/(2πτ2) ; φ=2 mm
220
2
0 )2/()(
)2/()(
δνννδνρνρ
+−=
πτπδν
*2**2
1 2
2
R==
Then:
J.s/m3
m3/J/s2
Large saturation: MHzBut much smaller than the Doppler width at 300 K (≅ 1000 MHz)
0 πτπ *2**2 2
cs
Pd
*2)( 0 ==∫
πδνρννρ
137823
2
20 10*7.6
10*25.6*10*3*)10(*
10*1*4
**
*4 −−
−
===π
ρRcs
P
1934
63921
3
12 10*3.710*6.6**8
10*6*)10*589(
8=== −
−
ππλ
h
AB 200
*1
12 ==R
BS
ρ
140*141* ==+= δνδνδν SS
- Velocity distribution function of Ar* metastable atoms in a helicon reactor
- Velocity distribution function of Ar* atoms in an expanding arc jet
- Velocity of Ar+ ions in ECR reactor
Examples of LIF experiments
- Velocity of Ar ions in ECR reactor
- Velocity distribution function of Xe+ in a Hall thruster
- Velocity of sputtered Al atoms under Ar+ ion bombardment
Velocity distribution function of Ar* metastable atoms in a Helicon reactor
0
-20
-40
N o6
N o5
Antenna between 4 and 5I1 to 6 =3,3,3,3,3,-4.5 A
Dis
tanc
e fr
om th
e ce
nter
of a
nten
na (
cm)
Quartz tube
Antenna
80
60
40
20
0
-50 0 50 100 150 200 250 300
N o5N o4
N o3
N o2
N o1
B fie ld ( G auss )
Dis
tanc
e fr
om th
e ce
nter
of a
nten
na (
cm)
Antenna
Laser beam
Recorded signals when the laser frequency is scanned
0.4
0.5
0.6
0.7
0.8
discharges on
discharges off
LASER ON
Sig
nal [
arb.
u.]
Laser IntensityLIF Signal
0 1000 2000 3000 4000 5000
0.0
0.1
0.2
0.3Fabry-Perot
discharges off
Sig
nal [
arb.
u.]
channel number
discharges onLASER OFF
For frequency calibration
Determination of the Doppler width
-0.015
-0.010
-0.005
0.000
-0.3
-0.2
-0.1
0.0
Ln
(I/I
0)
Ln
(I/I
0)
Cl2 + 10% Ar at 5 mTorr
-2 -1 0 1 2-0.035
-0.030
-0.025
-0.020
-2 -1 0 1 2-0.7
-0.6
-0.5
-0.4 Ln
(I/I
P=100 WT=404 K
Ln
(I/I
Frequency shift (GHz)
P=700 WT=572 K
MTc
MRTcGHzD /1016.7)/(2ln2)/2()(0
160 λ
νδν −⋅==
Line profile in presence of strong magnetic field
B=0
+1 0−1
B≠0
2p7
MB=0
+1 0−1
B≠0
2p2
M
Zeeman components of the absorbing lines of Argon
772.38 nm; 2p7 ← 3P2 line 772.42 nm; 2p2 ← 3P0 line
+2+1 0−1−2
1s5
σ+ σ−
π
01s3
σ+ σ−
π
Bkrr
⊥ if only σ+ and σ- lines existBErr
⊥if only π line (s) existBk
rr⊥ BE
rr//
then only σ+ and σ- lines existBkrr
//
helicon, 20W, 3,7sccmB strong
absorption between B2-B3772,38nm
B=146gauss0,2
0,25
0,3polarizationperpendicular to B
polarization parallel to B
σ, ∆ Μ = + 1
Experimental profiles of the 722.38 nm line with two different polarization fitted with Gaussians
B=146gaussT=248K
0
0,05
0,1
0,15
6 6,5 7 7,5 8 8,5frequency (GHz)
ln(I0
/I)
σ, ∆ Μ = − 1
π , ∆ Μ = 0
Reflexion of Ar* atoms on Pyrex surface
LIF signal near the surface fromlaser beam to the surface
R=0.28 ± 0.05
Velocity mapping of argon atoms (metastable) in an expanding cascaded arc jet
By Laser Induced Fluorescence technique & by absorptionby absorption
Experimental determination of argon atoms vdf in an expanding arc jet by LIF (Eindhoven)
cathode anode
gas
stationaryshock
M>>1 M<1
P = 5 kWTe = 1 eVne = 1022 m-3
psource = 5.104 Papbg = 10…100 Pa
Expected density and velocity distribution along the jet axis
Velocity
z
stationaryshock
Density
M>1 M<1
Laser Doppler-Shift setup
1.0
Argon lamp
inte
nsity
(a.
u.)
BSBS
chopperdiode laser
ArgonFabry
z-axis
1 2 3 4 5 6 7 8 9 10 11
0.0
0.5 Fabry Perot
LIF signal
inte
nsity
(a.
u.)
piezo voltage (a.u.)Lock in
amplifier
Argonlamp
FabryPerot
diodes
PMT
filter
reference
trigger
inte
nsity
(a.
u.)
0.5z=59 mm
0.0
0.5 z=46 mm
012
z=26 mm
Ar* velocity distribution functions
0.2
0.3
(axial v at axis center)
(radial v at z = 50 mm)
-1 0 1 2 3 4 5 60.00.51.01.5 z=174 mm
velocity (km/s)
inte
nsity
(a.
u.)
0.0
0.5
1.0 z=100 mm
0.0
0.5z=59 mm
-3 -2 -1 0 1 2 30.0
0.5
1.0
0.0
0.1
0.2
velocity (km/s)
inte
nsity
(a.u
.)
r=25 mm
r=0 mm
Velocity distribution of Ar + metastable ions in an ECR reactor
Electron Cyclotron Resonance reactor
In 1990th, the goal for µ-electronics industry is to separate the generation of the plasma from the energy of ions impinging on the substrate
- Electron Cyclotron Resonance ( ECR)- Helicon- Inductively coupled plasmas (ICP)
Pulsed versus CW laser for the LIF
Pulsed laser∆νL≅1 GHz
CW laser∆νL<0.1 GHz
Acceleration of Ar+ ions leaving the ECR zone
Azimuthal velocity of Ar+ ions due to the ExB Lorentz force
Velocity distribution function of Xe+
metastable ions in a Hall effect thruster
The 5 kW-class PPS®X000 thruster in the Pivoine facility
High power Hall Effect Thruster150 mm outer channel diameter40 mm channel lengthP = 2 – 6 kWUd = 200-1000 VΦa = 3 – 20 mg/s
Experimental arrangement
Energy diagram and LIF scheme for metastable Xe + ions
6p 2D
o5/2
air = 834.7233 nm
= 541 915 nm
113512.36 cm-1rad = 9.3 ns)
LIF bench: high-power tunable single-mode laser diode
5d 2F7/2
6s 2P3/2
air = 541.915 nm
BR = 0.9
101535.67 cm-1
95064.38 cm-1
Xe+
metastable level
9 stable istopes→ istopic shifts and HF structure
→ 19 components
Hypothesis: fluorescence profile = VDF
Detection branch
The fluorescence collectionlens housing and holder areat floating potential
1:1 imaging systemf = 40 mm lens200 µm core optical fiber
x-y high-precision long range translation stages
Trouble: optics pollution and wear
Example of the Steady-state on-axis development of the IVDF
0.5
1.0 x = 0 mm
x = -5 mm
x = -10 mm
Nor
mal
ized
ion
VD
F (
arb.
units
)
x = -15 mm
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0 5000 10000 15000 20000 25000 300000.0
0.5
1.0
Axial velocity (m/s)
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
x = 40 mm
x = 30 mm
x = 20 mm
x = 6 mm
Nor
mal
ized
ion
VD
F (
arb.
units
)
Macroscopic quantities
- mean velocity
- max velocity (10%)
- dispersion
σ×= )( 222 Lnp
20000
25000
30000
Ion
axia
l vel
ocity
(m
/s)
Comparison between hybrid model outcome and experim ental result
PPS®X000 thruster, 500V and 6 mg/s
The electron mobility through the magnetic barrier is inferred from
-20 -10 0 10 20 30 400
5000
10000
15000
20000
Ion
axia
l vel
ocity
(m
/s)
Axial position (mm)
hybrid modelling experiment
outcome of PIC simulations
IVD Characteristics of the HET in the oscillating regime The best performance
Anode discharge currentpower shutdown
τc = 10 µs
f = 2500 Hz
PPS100-LM Hall thrusterBN-SiO2 wallsUd = 250 VΦa = 4.5 mg/s xenon gasIc = 5 A forcedIc = 5 APback = 2×10-5 mbar-Xe
Discharge propertiesId = 4.1 Af = 21 kHz
PerformancesT = 69 mN (wo line cut)T = 67 mN (w line cut)
Id: ensemble averaged over 128 cycles
forcedoscillations
quasi-normaloscillations
linecut
restarting
Detection of LIF by Photon-counting technique
Requirements
to monitor the time evolution of the Xe+ VDF during a breathing oscillation time period (~20 kHz)
LIF tool with a time resolution < 1 µsnb of fluorescence photons during 1 µs ≈ 10-2 (with Plaser = 1 mW)nb of background photons during 1 µs ≈ 1
a) Photon-counting technique → high time resolutionb) Real time add and subtract operation with chopped laser beam → high S/N
Remote discharge current breakdischarge stability (quasi-periodic regime vs non-stationary regime)trigger for all devicesforced as well as natural oscillations
Temporal traces at different Ion velocities11 measurement locations along the channel axis
Time-averaged electric field on-axis distribution.The electric field is inferred from the mean ion velocity.
Extracted Time series for various velocity groups
Number of on/offcycles ~ 1M
Width of a velocitygroup:δv = 10 m/s
Between 10-15 points to reconstruct the local ion VDF
Validity of the measurement technique: Checkout
At each location, comparison between
Time-averaged IVDF measured by means of a lock-in detector ( τ = 1s; power cut)
Combining time-resolved IVDFs recorded with the photon counting technique
x = -2 mm x = 4 mm
Contour map of the IVDF(t)
anode dischargecurrent break restarting
Combining all velocity group time-series at a given measurement location
Velocity distribution of sputtered Aluminum atoms under Ar+ Bombardment
By Laser Induced Fluorescence technique
Sticking coefficient of sputtered Al atoms on trench side walls and on different surfaces strongly depends on their velocity (energy)
distribution.
Diode
LaserLIF
B.S.optical fiber LIF
Laser absorption and (LIF) with a Diode Laser
2S1/2
PD1
Diode Laser
Controler
PD2
Mono+ PMT
Lock-InOscilloscopesynchro
C.M.
xz
reference
substrat Al
-15 -10 -5 0 5 10 15
0,0
0,2
0,4
0,6
0,8
1,0
0.98 GHz
Inte
nsité
(u.
a.)
∆ν = ν − ν0 (GHz)
2S1/2
2P1/2
394.40 nmLIF
396.15 nmLASER
2P3/2
LIF
Energy diagram ofAl
Hyperfine structure of the 396.15 nm transition of Al atoms
2S1/2F=3
F=2 Total line
Hyperfine components:
4 to 3 3 to 3 3 to 2
2P3/22P1/2
394.40 nm
396.15 nm
F=4F=3F=2F=1
0.014 eV
-3 0 3ν - ν
0 (GHz)
3 to 2 2 to 3 2 to 2 1 to 2
-20 -15 -10 -5 0 5 10 15 20
-0.06
-0.03
0.00
ln (
I / I
0 )∆ν (GHz)
1 mTorr
-20 -15 -10 -5 0 5 10 15 20-0.12
-0.08
-0.04
0.00
ln (
I / I
0 )
∆ν (GHz)
2 mTorrFrom zero collision to thermalization
-20 -10 0 10 20
-0.04
-0.02
0.00
0.5 mTorr
ln (
I / I
0 )
∆ν (GHz)
Absorption line profile
∆ν (GHz)
-15 -10 -5 0 5 10 15
-0.2
-0.1
0.0
ln
( I
/ I0 )
5 mTorr
∆ν (GHz)-15 -10 -5 0 5 10 15
-0.8
-0.6
-0.4
-0.2
0.0
ln (
I / I
0 )
∆ν (GHz)
20 mTorr∆ν (GHz)
-15 -10 -5 0 5 10 15
-0.6
-0.4
-0.2
0.0
ln (
I / I
0 )
∆ν (GHz)
84 mTorr
Gas pressure (mTorr) 0.5 1 2
Collision mean free path (cm) 25 12 6
5 20 84
2.5 0.6 0.1
( ) dEdE
EE
EE
EdEdEf b
b
Ω
Λ+−
+×∝Ω
13 1cos),( θθ
Velocity distribution function of sputtered Atoms
Comparison with Thompson theoryof velocity distributions recorded at very low
argon pressure (0.4 mTorr)
LIF: distribution de Vangular distribution
-8 -6 -4 -2 0 2 4 6
0,00
0,01
0,02
0,03
velocity (km/s)
ln (
Io /
I )
Vz distribution (b)
Vx distribution (a)
Cosine(dashed
)Harte(solid)
LIF: Vz distribution
Eb surface binding energy
Under low energy bombardment (ICP), the angular distribution of sputtered Al atoms is much closer to a “Hart shape" than to a cosine distribution
θ (°C)
LIF: distribution de Vz
absorption: distribution de Vx
30
60
90-90
-60
-30
0 2 4 6 8 10
0,00
0,25
0,50
0,75
1,00
velocity (km/s)
Vz distribution (b)
LIF
inte
nsity
(a.
u)
LIF: Vz distribution
Absorption: V x distribution
Cosine(dashed)
Harte(solid)
Few References to consult- W. Demtröder, Laser Spectroscopy, 2nd Ed. (Springer, Berlin, 1996).
-N. Sadeghi, Molecular Spectroscopy Techniques Applied for Processing Plasma Diagnostics,J. Plasma & Fusion Research,
80 (2004) 767.- T. Nakano, N. Sadeghi, and R.A. Gottscho, Ion and neutral temperatures in electron cyclotron resonance plasma Reactors,Appl. Phys. Lett. 58 (1991) 458
- N. Sadeghi, T. Nakano, D.J. Trevor, and R.A. Gottscho, Ion transport in an electron cyclotron resonance plasma,J. Appl. Phys. 70 (1991) 2552- R Engeln, S Mazouffre, P Vankan, D C Schram and N Sadeghi, Flow dynamics and invasion by background gas of a supersonically expanding thermal plasma,Plasma Sources Sci. Technol. 10 (2001) 1.-P. Macko and N. Sadeghi, Determination of the non-relaxation (reflection) probability of metastable Ar(3P2) atoms on aPyrex surface, Plasma Sources Sci. Technol. 13 (2004) 303- G. Cunge, R. Ramos, D. Vempaire, M. Touzeau, M. Neijbauer, and N. Sadeghi, Gas temperature measurement in CF4, SF6, O2, Cl2, and HBr inductively coupled plasmas, JVST A 27 (2009) 471- R Ramos, G Cunge, M Touzeau and N Sadeghi, Measured velocity distribution of sputtered Al atoms perpendicular and- R Ramos, G Cunge, M Touzeau and N Sadeghi, Measured velocity distribution of sputtered Al atoms perpendicular andparallel to the target, J. Phys. D: Appl. Phys. 41 (2008) 152003- E. Despiau-Pujoa, P. Chabert, R. Ramos, G. Cunge, and N. Sadeghi, Velocity distribution function of sputtered gallium atoms during inductively coupled argon plasma treatment of a GaAs surface, JVST A 27 (2009) 356
- G. Cunge, D. Vempaire, and N. Sadeghi, Gas convection caused by electron pressure drop in the afterglow of a pulsed inductively coupled plasma discharge, App. Phys. Lett. 96 (2010) 131501
- D. Gawron, S. Mazouffre, N. Sadeghi and A. Héron, Influence of magnetic field and discharge voltage on the acceleration layer features in a Hall effect thruster, Plasma Sources Sci. Technol. 17 (2008) 025001
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